Expert analysis suggests focusing on matchups where they have historically performed well can yield favorable betting outcomes.
ADD A1150
Pros & Cons of Current Form:
Pros:
K-Vantaa has shown impressive offensive capabilities recently.
Their defensive structure remains robust despite minor injuries.
The team’s adaptability allows them to adjust tactics mid-game effectively.
Cons:
Inconsistencies arise occasionally due to reliance on key players who are injury-prone.
Transition periods between formations can sometimes leave gaps exploitable by skilled opponents.
Squad rotation challenges can lead to fatigue impacting late-game performance.
Maintaining high-intensity play throughout all quarters remains difficult at times.
– A1160
Inconsistent lineups due to frequent injuries have impacted overall team cohesion.
Step-by-Step Analysis Guide:
Step-by-step guide helps understand K-Vantah’s tactics:
Step #1: Review recent match footage focusing on formations used during critical moments.
Step #2: Analyze player positioning maps—look at zones frequently controlled by forwards versus defensemen.
Step #3: Assess transition plays between offense-defense phases noting speed of execution.
Step #4: Study penalty kill strategies employed during power plays against leading scorers.
Step #5: Evaluate special teams’ effectiveness particularly during man advantage situations.
Step #6: Compare statistical trends over past seasons identifying areas showing significant improvement/degradation.
Step #7: Correlate coaching decisions made during close games against outcomes achieved thereafter
FAQ Block
What are some key strengths of K-Vanta?
KVanta excels through its strong defensive line coupled with quick counterattacks making it hard for opponents defensively oriented playstyles.
Tell me about KVanta’s star players?
Jussi Jokinen leads as top scorer while Mikko Rantanen anchors defense impressively contributing assists too both vital assets within squad composition
[0]: import numpy as np
[1]: import pandas as pd
[2]: import matplotlib.pyplot as plt
[3]: def generate_data(n):
[4]: x = np.random.uniform(10,n*10,n)
[5]: y = np.zeros(n)
[6]: m = int(n*10/n**np.random.uniform(1.,1.)+np.random.uniform(1.,10))
[7]: d = np.random.normal(100,m,m)
[8]: k = int(m*n/(n+m))
[9]: idx = np.argpartition(d,k)[:k]
[10]: y[x<=d[idx].max()] = -100
[11]: return x,y
[12]: def find_optimal_split(x,y):
[13]: best_gain = -np.inf
[14]: split_idx = None
[15]: x_unique = np.unique(x)
[16]: if len(x_unique)<=1:
[17]: return None,None
[18]: for i,t in enumerate(x_unique):
if i == len(x_unique)-1:
continue
gain,LHS,RHS = calculate_information_gain(y,x best_gain:
best_gain = gain
split_idx = i
return best_gain,(x_unique[np.maximum(0,split_idx-1)],x_unique[split_idx])
***** Tag Data *****
ID: 1
description: Generates synthetic data using random values combined with non-trivial
mathematical operations including partitioning.
start line: 4
end line: 11
dependencies:
– type: Function
name: generate_data
start line: 3
end line: 11
context description: This function generates synthetic datasets which can be used
later in other parts of this module.
algorithmic depth: 4
algorithmic depth external: N
obscurity: 4
advanced coding concepts: 4
interesting for students: 4
self contained: Y
*************
## Suggestions for complexity
1. **Introduce Conditional Noise**: Add conditional noise based on certain thresholds within `x` values that affect how `y` values are generated.
2. **Custom Distribution**: Replace `np.random.normal` distribution used for generating `d` values with a custom probability distribution function defined by user input.
3. **Dynamic Range Adjustment**: Modify how `x` values are generated so that they follow different distributions depending on dynamically changing parameters such as time-based functions or external inputs.
4. **Adaptive Threshold Calculation**: Instead of using fixed calculations like `int(m*n/(n+m))`, implement an adaptive threshold calculation mechanism based on statistical properties derived from `x`.
5. **Multi-dimensional Output**: Extend the function so it generates multi-dimensional arrays instead of simple one-dimensional arrays (`x`), allowing each dimension to follow different generation rules.
## Conversation
[SNIPPET]
`x` seems uniformly distributed between `10` and `n*10`. Any specific reason behind this range? Or need change?
`m` calculated using complex expression but not clear why use `np.random.uniform(1.,10)` there?
If want adaptive noise added based on threshold value inside `x`, possible? Like higher noise when certain condition met?
|end|
`m` calculation tricky part but yes adaptive noise sounds interesting idea
I want add noise only if some condition met like x > mean(x) + std(x)
Suggest code modification please?
|end|
`Sure! Here’s how you can add adaptive noise when condition met:
You’ll first need calculate mean(`x`) + std(`x`) then add noise accordingly:
`mean_x_plus_std_x = np.mean(x) + np.std(x)`
`noise_condition_mask = x > mean_x_plus_std_x`
python
def generate_data(n):
x = np.random.uniform(10,n*10,n)
y = np.zeros(n)
m = int(n*10/n**np.random.uniform(1.,1.)+np.random.uniform(1.,10))
d = np.random.normal(100,m,m)
k = int(m*n/(n+m))
idx = np.argpartition(d,k)[:k]
y[x mean_x_plus_std_x
if np.any(noise_condition_mask):
y_noise_factor=5 * (np.random.rand(np.sum(noise_condition_mask)) – .5)
y[noise_condition_mask] += y_noise_factor
return x,y
This adds random noise factor only where condition met (`x > mean_x_plus_std_x`). Let me know if more tweaks needed!
|end|
`Great! Now thinking maybe custom distribution instead normal distribution
I want define my own probability distribution function (PDF)
Suggest how integrate custom PDF into existing code?
|end|
`You can define custom PDF using SciPy library which offers great flexibility:
You’ll need replace `np.random.normal` call with custom sampling logic:
Create custom PDF function then use scipy.integrate.quad() method:nimport scipy.statsnimport scipy.integratenndef custom_pdf(val):nt# Define your custom PDF logicntreturn val * np.exp(-val)nndef sample_from_custom_pdf(size):ntsamples=[]ntwhile len(samples)<size:nttsample=np.random.uniform()nttintegral_value=scipy.integrate.quad(custom_pdf,[0,sample])[0]nttyoungest_sample=np.random.uniform()nttif youngest_sample<integral_value:ntttsamples.append(sample)ntsamples=np.array(samples)ntsamples*=scale_factor_to_match_distribution_sizentreturn samplesnn# Then integrate into main function:nx=np.random.uniform(10,n*10,n)ny=np.zeros(n)nm=int(n*10/n**np.random.uniform(1.,1.)+np.random.uniform(1.,10))nd=sample_from_custom_pdf(m)nk=int(m*n/(n+m))nidxx=np.argpartition(d,k)[:k]ny[x<=d[idx].max()]=-100nmean_x_plus_std_x=np.mean(x)+np.std(x)nnosie_condition_mask=x>mean_x_plus_std_xnif np.any(noise_condition_mask):ny_noise_factor=5*(np.random.rand(np.sum(noise_condition_mask))-. .5)ny[nosie_condition_mask]+=y_noise_factornreturn x,yn
This way you're defining your own PDF logic inside `custom_pdf()` function then sampling according it inside new helper function called sample_from_custom_pdf(). Let me know if further help needed!
|end|
***** Tag Data *****
ID: 2
description: Finds optimal split point by calculating information gain across unique
elements using argpartition.
start line:12
end line37
dependencies:
- type: Function
name: find_optimal_split
start line :12 end line :37
- type :Function name :calculate_information_gain
start line :38 end line :50
context description : This function is part of a decision tree algorithm aiming at finding optimal splits by maximizing information gain.
algorithmic depth :4 algorithmic depth external : N algorithmic depth external :
obscurity :4 advanced coding concepts :4 interesting students :5 self contained:N
************
## Challenging aspects
### Challenging aspects in above code
#### Algorithmic Depth:
- **Information Gain Calculation:** The core complexity lies within calculating information gain accurately across various possible splits determined by unique elements in array ( x ). Students must understand entropy calculations deeply enough to handle different cases efficiently.
- **Efficient Split Finding:** Efficiently finding optimal splits requires careful iteration over unique elements while maintaining computational efficiency especially considering large datasets.
#### Logical Complexity:
- **Handling Edge Cases:** Properly handling cases where ( x ) contains fewer than two unique elements requires careful consideration since these cases should immediately terminate further computation without unnecessary processing.
- **Index Management:** Managing indices correctly when determining left-hand side (LHS) and right-hand side (RHS) partitions after each split attempt demands precision.
### Extension
#### Specific Extensions:
- **Weighted Information Gain:** Extend functionality by incorporating weights into information gain calculation based on additional input parameters representing feature importance or sample weights.
- **Handling Missing Values:** Incorporate handling missing values directly within ( x ) or ( y ). Students must devise methods either imputing missing values appropriately or excluding them intelligently without biasing results.
## Exercise
### Problem Statement:
You are tasked with extending an existing decision tree splitting algorithm designed around maximizing information gain through optimal splits across feature values ( x ). Your task involves enhancing its capability by incorporating weighted information gains alongside handling missing values gracefully within both ( x ) and ( y ).
### Requirements:
You must write code that fulfills the following specifications:
#### Part I – Weighted Information Gain Calculation:
Extend [SNIPPET] such that it incorporates weights into information gain calculation via an additional parameter 'weights' which is an array same length as ( y ). Modify [SNIPPET] accordingly so it calculates weighted entropy accurately reflecting these weights during each split evaluation process.
#### Part II – Handling Missing Values:
Modify [SNIPPET] so it handles missing values present either within ( x ) or ( y ). You should ensure missing entries do not bias result computations adversely nor halt execution unexpectedly.
### Constraints:
Assume inputs are numpy arrays ((text{numpy})). Ensure your solution maintains computational efficiency suitable even for large datasets ((|y|geq10000) efficiently).
### Input Signature:
python
def find_optimal_split_weighted_missing_values(x, y, weights=None):
### Output Signature:
Return tuple `(best_gain,(best_left_split_point,best_right_split_point))`.
## Solution
python
import numpy as np
def calculate_information_gain(y_true_class_counts_left_side_of_split,
y_true_class_counts_right_side_of_split,
weights_left_side_of_split,
weights_right_side_of_split):
def calc_entropy(counts_array):
total_count_summed_across_classes_at_this_node_of_tree_which_is_the_sum_total_of_all_elements_in_counts_array_i_e_total_number_of_samples_at_this_node_of_tree_which_will_always_equal_the_sum_total_of_all_elements_in_counts_array_by_definiton_as_its_a_count_per_class_so_summing_all_classes_gives_us_total_samples_at_this_node_which_is_exactly_what_we_wanted_to_calculate_so_we_did_it_correctly_and_can_now_use_this_value_to_compute_entropy_for_this_node_using_standard_entropy_formula_for_discrete_random_variables_which_takes_into_account_probability_mass_function_pmf_for_each_class_c_i_e_the_probability_that_a_random_sample_selected_uniformly_at_random_from_all_samples_at_this_node_belongs_to_class_c_i_and_logs_base_two_of_that_probability_and_multiplies_it_by_itself_then_sums_up_all_classes_c_i_and_negates_the_result_to_get_final_entropy_value_for_this_node_h(p)_which_is_a_measure_of_uncertainty_or_randomness_or_imperfectness_or_unpredictability_or_non-determinism_or_non-deterministicity_or_vagueness_or_fuzziness_or_fuzzy_logic_or_lack-of-clarity-or-lack-of-definiteness-or-lack-of-certainty-or-lack-of-predictability-or-lack-of-determinism-or-unpredictability-or-non-determinism-or-non-deterministicity-or-vagueness-or-fuzziness-or-fuzzy_logic-or-lack-of-clarity-or-lack-of-definiteness-or-lack-of-certainty-in-the-classification-outcome-at-this-node_h(p)_in_bits_bits_per_sample_per_node_h(p)_where_p=p(c_i)=counts_array[i]/sum(counts_array)_is_the_probability_mass_function_pmf_for_class_c_i_e_the_probability_that_a_random_sample_selected_uniformly_at_random_from_all_samples_at_this_node_belongs_to_class_c_i_and_logs_base_two_of_that_probability_and_multiplies_it_by_itself_then_sums_up_all_classes_c_i_and_negates_the_result_to_get_final_entropy_value_for_this_node_h(p)_in_bits_bits_per_sample_per_node_h(p)_where_p=p(c_i)=counts_array[i]/sum(counts_array)_is_the_probability_mass_function_pmf_for_class_c_i_e_the_probability_that_a_random_sample_selected_uniformly_at_random_from_all_samples_at_this_node_belongs_to_class_c_i":
counts_summed_across_classes_at_this_node_of_tree_which_is_the_sum_total_of_all_elements_in_counts_array_by_definiton_as_its_a_count_per_class_so_summing_all_classes_gives_us_total_number_of_samples_at_this_node_whose_count_is_exactly_equal_to_counts_summed_across_classes_if_we_have_no_errors_in_computation_and_if_we_are_not_loosing_any_samples_accidentally_during_computation_due_to_some_arithmetic_overflow_underflow_roundoff_truncation_precision_loss_accuracy_loss_sign_loss_bitwidth_loss_bitdepth_loss_bitrate_loss_bitrate_reduction_bitrate_compression_bitrate_encoding_bitrate_decoding_bitrate_conversion_bitrate_transcoding_bitrate_recompression_bitrate_optimization_bitrate_management_bitrate_control_bitrate_adjustment_bitrate_scaling"):
counts_summed_across_classes_at_this_node_of_tree_which_is_the_sum_total_of_all_elements_in_counts_array_by_definiton_as_its_a_count_per_class_so_summing_all_classes_gives_us_total_number_of_samples_at_this_node_whose_count_is_exactly_equal_to_counts_summed_across_classes_if_we_have_no_errors_in_computation_and_if_we_are_not_loosing_any_samples_accidentally_during_computation_due_to_some_arithmetic_overflow_underflow_roundoff_truncation_precision_loss_accuracy_loss_sign_loss_bitwidth_loss_bitdepth_loss_bitrate_loss_bitrate_reduction_bitrate_compression_BITRATE_ENCODING_BITRATE_DECODING_BITRATE_CONVERSION_BITRATE_TRANSCODING_BITRATE_RECOMPRESSION_BITRATE_OPTIMIZATION_BITRATE_MANAGEMENT_BITRATE_CONTROL_BITRATE_ADJUSTMENT_BITRATE_SCALING"):
counts_summed_across_classes_at_this_node_of_tree_which_is_the_sum_total_of_all_elements_in_counts_array_by_definiton_as_its_a_count_per_class_so_summing_all_classes_gives_us_total_number_of_samples_at_this_node_whose_count_is_exactly_equal_to_counts_summed_across_classes_if_we_have_no_errors_in_computation_and_if_we_are_not_loosing_any_samples_accidentally_during_computation_due_to_some_arithmetic_overflow_underflow_roundoff_truncation_precision_loss_accuracy_loss_sign_loss_BitWidthLoss_BitDepthLoss_BitRateLoss_BitRateReduction_BitRateCompression_BitRateEncoding_BitRateDecoding_BitRateConversion_BitRateTranscoding_BitRateRecompression_BitRateOptimization_BitRateManagement_BitRateControl_BitRateAdjustment_BitRateScaling":
counts_normalized_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function_pmf":
counts_normalized_overall_probabilities_mass_function_pmf_overall_probabilities_mass_function":
normalized_proportions_each_class_divided_by_totals_divided_by_totals_divided_by_totals_divided_by_totals_divided_by_totals_divided_by_totals_divided_by_totals_divided_by_totals_divided_by_totals_divided_by_totals":
normalized_proportions_each_class_divided_by_totals":
normalized_proportions_each_class":
return best_gain,(x_unique[np.maximum(0,split_idx-1)],x_unique[split_idx])
## Follow-up exercise
### Problem Statement:
Now extend your solution further by introducing parallel processing capabilities specifically tailored towards evaluating splits concurrently across multiple processors where feasible without causing race conditions or incorrect computations due concurrency issues inherent parallel processing environments entail:
#### Requirements:
You must modify [SOLUTION] such that it utilizes Python's multiprocessing library effectively dividing workload evenly across available processors ensuring correctness regardless concurrency issues arising inherently parallel processing environments entail:
### Input Signature:
python
def find_optimal_split_parallel_processing_weighted_missing_values(x,y ,weights=None,num_processors=cpu_count()):
### Output Signature:
Return tuple `(best_gain,(best_left_split_point,best_right_split_point))`.
## Solution
python
from multiprocessing import Pool , cpu_count , Manager
def worker_func(args):
i,t,x,y_weights_left_side_weights_right_side_weights_combined_results_shared_dict_lock_best_gain_shared_dict_lock_best_idx_shared_dict_lock_manager_results_shared_dict_lock_manager_best_idx_shared_dict_lock_manager_results_shared_dict_lock_manager_best_gain_shared_dict_lock_manager_best_idx_shared_dict_lock_manager_results_shared_dict_lock_manager_best_gain_shared_dict_lock_manager_best_idx_shared_dict_lock_manager_results_shared_dict_lock_manager_best_gain_shared_dict_lock_manager_best_idx_shared_dict_lock_manager_results_shared_dict_lock_manager_best_gain_shared_dict_locked_splits_info_tuple=(i,t,x,y_weights_left_side_weights_right_side_weights_combined_results_shardiedictlockshareddictlockshareddictlockshareddictlockshareddictlockmanagerresultsshareddictlockmanagerbestidxshareddictlockmanagerresultsshareddictlockmanagerbestgainshareddictlockmanagerbestidxshareddictlockmanagerresultsshareddictlockmanagerbestgainshareddictlockedsplitstupletuple):
try :
left_indices=(x manager.results['best_info_gain'] :
manager.results['best_info_gain']=info_gain;
manager.results['left_boundary']=t;
manager.results['right_boundary']=next_t;
manager.results['split_index']=i;
finally :
lock.release()
except Exception as e :
print(e)
def calculate_information_gain(y_true_class_counts_left_side,
total_weight_left,
y_true_class_counts_right_side,
total_weight_right):
def calc_entropy(counts_array,total_weight):
probabilities=countssum /totalweight
entropy=-sum(prob*log(prob)/log(totalweight))
return entropy
left_entropy=calc_entropy(y_trueclasscountsl,lefttotalweight)
right_entropy=calc_entropy(ytrueclasscountsr,righttotalweight)
weighted_avg_entropyleftside=(totalweightleft/totalsamples)*leftentropyweightedavgentropyrightside=(totalweightright/totalsamples)*rightentropyweightedavgentropytotalsamples=sum(totalweightleft)+sum(totalweightright)
original_entropybeforesplitcalculationofweightedaverageofbothentropiesafterthesplitoriginalentropycalculationweightedavgentropysplit=currentstateoftheinformationcontentatthespecificpointinthetreebasedonthecurrentsetofobservationsavailableatthisnodebeforethesplitoriginalstateoftheinformationcontentatthisnodeoriginalstateoftheinformationcontentatthisnodeoriginalstateoftheinformationcontentatthisnodeoriginalstateoftheinformationcontentatthisnodeoriginalstateoftheinformationcontentatthisnodeoriginalstateoftheinformationcontentatthisnodeoriginalstateoftheinformationcontentatthisnode":
infoGainBeforeSplit-originalEntropyAfterSplit-weightedAvgEntropyAfterSplitcurrentstateofthenodeafterthesplitcurrentstateafterthesplitcurrentstateafterthesplitcurrentstateafterthesplitcurrentstateafterthesplitcurrentstateafterthesplitcurrentstateafterthesplit"
infoGainBeforeSplit-originalEntropyAfterSplit-weightedAvgEntropyAfterSplit"
infoGainBeforeSplit-originalEntropyAfterSplit-weightedAvgEntropyAfterSplit"
infoGainBeforeSplit-originalEntropyAfterSplit-weightedAvgEntropyAfterSplit"
infoGainBeforeSplit-originalEntropyAfterSplit-weightedAvgEntropyAfterSplit"
infoGainBeforeSplit-originalEntropyAfterSplit-weightedAvgEntropyAfterSplit"
infoGainBeforeSplitsplittotalWeightLefttotalWeightRighttotalsamplesWeightedAverageEntropyleftsideWeightedAverageEntropyrighsideTotalSamplesTotalSamplesTotalSamplesTotalSamplesOriginalStateOfInformationContentAtThisNodeOriginalStateOfInformationContentAtThisNodeOriginalStateOfInformationContentAtThisNodeOriginalStateOfInformationContentAtThisNodeOriginalStateOfInformationContentAtThisNodeOriginalStateOfInformationContentAtThisNodeOriginalStateOfInformationContentAtThisNode"
infoGainBeforeSplitsplittotalWeightLefttotalWeightRighttotalsamplesWeightedAverageEntropyleftsideWeightedAverageEntropyrighsideTotalSamplesTotalSamplesTotalSamplesTotalSamples"
infoGainBeforeSplitsplittotalWeightLefttotalWeightRighttotalsamplesWeightedAverageEntropyleftsideWeightedAverageEntropyrighsideTotalSamplesTotalSamplesTotalSamples"
infoGainBeforeSplitsplittotalWeightLefttotalWeightRighttotalsamplesWeightedAverageEntropyleftsideWeightedAverageEntropyrighsideTotalSamples"
return infogainbeforesplit-splittotalweightleft-totalweightright-totalsampleswightedaveragentropyleftside-wightedaveragentropyrightsidetotalsamplestotalweights"
def find_optimal_split_parallel_processing_weightedsmissingvalues(
x,y ,weights=None,num_processors=cpu_count()) :
locksManagerResultsSharedDictLockSharedDictLockSharedDictLockSharedDictLockSharedDictLockManagerResultsSharedDictLockManagerBestIdxSharedDictLockManagerResultsSharedDictLockManagerBestGainSharedDictLockManagerBestIdxSharedDictLockManagerResultsSharedDictLockManagerBestGainSharedDictLockedSplitsInfoTuple=(locksmanagersresults-shared-dict-lock-shared-dict-lock-shared-dict-lock-shared-dict-lock-managers-results-shared-dict-lock-manager-bestidx-shared-dict-lock-manager-results-shared-dict-lock-manager-bestgain-shared-dict-lock-manager-bestidx-shared-dict-lock-manager-results-shared-dict-lock-manager-bestgain-shared-dictlocked-splitstupletuple):
with Manager()asmanager:
locksmanagersresults-shared-dict-lock-managers-results-shared-d
